Infinite coordination polymer particles (ICPs) represent an area of growing interest in chemistry and materials science due to their unique and highly tailorable properties. These structures can be conveniently synthesized in high yields from the appropriate metal salts and bifunctional ligand precursors. Unlike conventional metal-organic framework materials (MOFs), these ICPs exhibit a higher level of structural tailorability, including size- and morphology-dependent properties, and therefore, the promise of a wider scope of utility. A variety of methods now exist for making numerous compositions, with modest control over particle size and shape. These structures can exhibit microporosity, tunable fluorescence, magnetic susceptibility, and unusual catalytic activity and selectivity. Perhaps most importantly, many of these ICP structures can be depolymerized (sometimes reversibly) much faster and under milder conditions than MOFs, which makes them attractive for a variety of biomedical applications. Thus far, several types of ICPs have been explored as contrast agents for magnetic resonance imaging and drug delivery systems. The groundwork for this emerging field of ICPs has been laid only in the past few years, yet significant advances have already been made. Indeed, this tutorial review introduces the reader to the field of ICPs, providing a guide to the work done so far, with an emphasis on synthesis, applications and future prospects.